X-rays of wavelength 0.240 nm are scattered from a free electron at rest and the resulting scattered photons have wavelength 0.244 nm. Through what angle did these photons scatter relative to the initial direction?
A) 130°
B) 80°
C) such scattering is impossible
D) 34°

Question

Quizplus · Accepted Answer

The increase in wavelength ($\Delta \lambda = 0.004$ nm) due to the scattering of X-rays by a free electron can be explained by the Compton effect, which describes the change in wavelength of photons when they are scattered by particles such as electrons. The formula for the Compton shift is $\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos \theta)$, where $h$ is Planck's constant, $m_e$ is the electron mass, $c$ is the speed of light, and $\theta$ is the scattering angle. Given the values, solving for $\theta$ yields an angle close to 130°, indicating that the photons were scattered through this angle relative to their initial direction.

X-Rays of Wavelength 0